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Thermalization and pseudolocality in extended quantum systems

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QIMW01 - Quantum integrable models in and out of equilibrium

The age-old questions of when and how thermalization occurs in extended systems have received a large amount of attention recently. It has been found that many integrable models, because of the presence of infinitely many conservation laws, display generalized thermalization: generalized Gibbs ensembles (GGE) describe equilibration states after long time evolutions with short-range Hamiltonians. It was also found that extended concepts of locality, such as those of pseudolocal and quasilocal conserved charges, were sometimes involved in GGEs. In this talk I will discuss my recent results in this subject. Using precise definitions of pseudolocal charges and GGEs, I will describe simple conditions on the time-evolved state and the dynamical response functions that guarantee generalized thermalization. I will explain in which cases this implies ordinary (Gibbs) thermalization. The results are based on studying a family of states defined by paths whose tangents are pseudolocal ch arges. The framework does not involve integrability, and all results are mathematically rigorous.

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